Mask induced polarization
Andrew Estroff, Yongfa Fan, Anatoly Bourov, Frank Cropanese,
Neal Lafferty, Lena Zavyalova, Bruce Smith
Rochester Institute of Technology, Microelectronic Engineering,
Rochester, NY 14623
ABSTRACT
The objective of this paper is to study the polarization induced by mask structures. Rigorous coupled-wave analysis
(RCWA) was used to study the interaction of electromagnetic waves with mask features. RCWA allows the
dependence of polarization effects of various wavelengths of radiation on grating pitch, profile, material, and thickness
to be studied. The results show that for the five different mask materials examined, the material properties, mask pitch,
and illumination all have a large influence on how the photomask polarizes radiation.
Keywords: Photomask, Polarization, Immersion Lithography, High NA, Wire-Grid Polarizer
1. INTRODUCTION
As smaller device dimensions are explored with ever increasing numerical apertures, polarization effects at the mask
plane become a concern. For a targeted half pitch resolution of hp, where:
0.5λ
hp =
,
(1)
(σ + 1) ⋅ NA
the pitch values (Λ) on a photomask are driven to dimensions multiplied by the optical system reduction as:
λ ⋅M
Λ mask =
(σ + 1) ⋅ NA
(2)
Assuming M = 4 , NA = 0.85 , and σ = 1.0 for current generation tools, Λ mask = 2.35 ⋅ λ . Next generation tools
moving towards NA = 1.2 will result in a minimum mask period of 1.67 ⋅ λ , at which point there can be more
significant polarization effects contributed by the photomask. The purpose of this paper is to examine these polarization
effects induced by the mask features at various numerical apertures, wavelengths, mask pitches, and for different
materials.
2. HIGH NA IMAGING AND POLARIZATION
2.1 High NA
TE polarization is defined as polarization perpendicular to the plane of incidence. Radiation polarized in the plane of
incidence is referred to as TM polarized. This is shown in Figure 1. As NA increases, the angle of incidence at the
wafer’s surface becomes more oblique. For TE polarization, there is no decrease in image contrast due to increased
angle of incidence. For TM polarization, as the angle of incidence approaches forty-five degrees, the image contrast
decreases until it reaches zero at forty-five degrees. This clearly highlights the importance of incorporating polarization
into lithography modeling and simulation. Smith and Cashmore have demonstrated the invalidity of a previously useful
metric (aerial image evaluation) in systems incorporating high NA and polarization[1].
TM
TE
Air
Fused Silica
Attenuated Phase Shift Mask (APSM) Material or
Binary Cr-O-N Stack
+1
0
-1
Figure 1. Unpolarized light incident upon photomask
2.2 Wire Grid Polarization
Wire-grid polarizers function according to the following basic principles. The electric field of the TE polarized light
induces a current in the wires. The forward transmitted radiation is out of phase with the incident TE wave and thus has
greatly reduced intensity, and the backward transmitted radiation is measured as the reflected wave. The electric field
of the TM polarized light is perpendicular to the wires. The wires are very narrow in this dimension and the electrons
have very little room to move. Therefore, most of the TM radiation is transmitted unaffected[2]. This is shown in
Figure 2.
Wave Parallel
to Wires
in Polarizer
Wave Orthogonal
to Wires
in Polarizer
Wave Orthogonal
to Wires
in Polarizer
Figure 2. Wire-Grid Polarization
The parameters which impact the efficiency of a wire-grid polarizer include period, duty cycle, thickness, shape, and
material. The grating period is the most important of these parameters as it determines the minimum wavelength that
can be polarized for a specific diffracted order, as shown in Equation 3. As the period decreases, wires become closer
together making it easier for TE polarization to induce a current in the wires. Additionally, narrower wires attenuate the
TM mode less, thus passing TM polarization more efficiently. Duty cycle is defined as the wire width divided by the
period. Assuming a fixed period, if the duty cycle increases, so does the wire width, attenuating both the TE and TM
polarizations more. Again, as in the case for decreasing period, a larger duty cycle will result in a more efficient TM
polarizer. As grating thickness increases, the wires are able to generate more current, creating a more efficient
polarizer. The shape of the wires also has an effect on the transmission and polarization efficiency. Non-vertical
sidewalls cause a decrease in transmission, but do not have much effect on the polarization efficiency. Rounded edges
will slightly reduce transmission, however, with greater rounding, there is a greater loss in transmission. Rounded
edges will also shift the peak transmission to shorter wavelengths. Most importantly, rounded edges will result in a
decrease in polarization efficiency, a benefit to the lithographer.
Wood first noticed a sharp decrease in transmission in the transition region of wire-grid polarizers in 1902.[3] This
phenomenon became known as Wood’s Anomalies. In 1907, Lord Rayleigh analyzed Wood’s data and noted that for a
specific wavelength ( λ ), period ( Λ ), material refractive index ( n ), and angle of incidence ( θ ), a higher diffracted
order ( m ) emerges, as [4]:
Λ ⋅ (n ± sin θ )
λ=
(3)
m
Another phenomenon that occurs in the transition region for wire-grid polarizers is the transmission of TE polarization
as opposed to TM polarization in Chromium gratings. These have been studied by Honkanen et al, and are
appropriately named inverse polarizers [5].
2.3 Mask induced polarization
Asymmetry is what gives rise to polarization due to the different behaviors of orthogonally polarized incident waves. In
photomasks the asymmetry is contributed to by the dimensions of the features. These features can not be sufficiently
approximated by assuming that they are a grating comprised of a thin metal film on a dielectric substrate. For feature
sizes greater than twice the wavelength, a diffraction grating results with little to no polarization effects. For feature
sizes less than half of the wavelength, the mask acts as a zero order wire-grid polarizer. Between half and twice the
wavelength is a transition region where the mask polarizes and diffracts the radiation, and can act as an inverse polarizer
for some materials.
3. EXPERIMENTAL SETUP
This purpose of this experiment is to demonstrate the polarization effects induced by a photomask. A binary CrxOyNzon-glass mask was modeled using an effective media approximation using data from materials deposited via magnetron
sputtering and characterized using ultra-violet variable angle spectroscopy (UV-VASE) [6]. The four layer stack
described in Tables 1 and 2 represent the graded CrxOyNz stack.
Cr
CrN
CrOx
Layer 1
Layer 2
Layer 3
Layer 4
90.00%
10.00%
0.00%
18.90%
2.10%
79.00%
9.45%
1.05%
89.50%
0.00%
0.00%
100.00%
Table 1. Cr-O-N stack composition. Layer 1 is closest to substrate, layer 4 is furthest.
n
k
Thickness (A)
Layer 1
193nm
0.8209
1.1825
500
Layer 2
193nm
1.5649
0.4121
133
248nm
0.8863
1.8700
500
248nm
1.8142
0.7391
133
Layer 3
193nm 248nm
1.6740 1.9734
0.3597 0.6584
133
133
Layer 4
193nm
1.7782
0.3148
133
248nm
2.1260
0.5918
133
Table 2. Cr-O-N stack data. Layer 1 is closest to substrate, Layer 4 is furthest.
Attenuated Phase Shifting Mask (APSM) materials were also modeled. APSM materials chosen were Tantalum Nitride
in a Silicon Nitride host (TaN-Si3N4), Molybdenum Oxide in a Silicon Dioxide host (MoO3-SiO2), Silicon in a Silicon
Nitride host (Si-Si3N4), and Tantalum Oxide in a Silicon Dioxide host (TaO5-SiO2). These materials were also modeled
using the effective media approximation described earlier. All masking films were designed for a π phase shift and
10% transmission. Tables 3 and 4 contain the APSM material data.
TaN-Si3N4
TaN
Si3N4
157nm
193nm
248nm
X
17.0%
27.0%
X
83.0%
73.0%
Si
Si-Si3N4
Si3N4
X
9.0%
10.0%
X
91.0%
90.0%
MoO3-SiO2
MoO3
SiO2
Ta2O5-SiO2
Ta2O5
SiO2
10.0%
30.0%
27.0%
11.5%
X
X
90.0%
70.0%
73.0%
88.5%
X
X
Table 3. APSM material composition. Host material in bold and italics.
MoO3-SiO2
TaN-Si3N4
Si-Si3N4
193nm 248nm 193nm 248nm 157nm 193nm 248nm
n
k
Thickness (A)
% Transmission
2.5626
0.489
631
9.88
2.3833
0.433
913
10.37
2.4317
0.4462
687
10.4
2.3482 1.6253 1.5891
0.4246 0.223 0.2117
936
1262
1647
10.35
9.8
9.69
1.6458
0.2246
1932
10.28
Ta2O5-SiO2
157nm
1.704
0.2468
1122
10.02
Table 4. APSM material data.
Rigorous Coupled Wave Analysis (RCWA) provides an exact solution for Maxwell’s equations [7]. Several
commercially available grating simulation software packages have emerged using RCWA. GSOLVER was used to
perform this experiment [8]. GSOLVER is a visual grating structure editor utilizing full 3-dimensional vector code
using hybrid RCWA and modal analysis and is capable of analyzing arbitrary grating thickness, number of materials,
and material index of refraction. Additionally, it is capable of modeling multiple materials, buried structures, and varied
shapes (represented by stacked layers).
Unpolarized radiation was modeled by first inputting a 100% TE polarized beam and measuring the transmitted TE
intensity in the 0th and 1st diffracted orders and then inputting a 100% TM polarized beam and measuring the transmitted
TM intensity in the 0th and 1st diffracted orders. This was done for 157nm, 193nm, and 248nm radiation depending on
the mask material. The mask pitch was varied from 0nm to 1000nm (1um) in 10nm increments, while the duty cycle
was kept fixed at 0.5. Degree of Polarization (shown in equation 4 below) was plotted versus mask pitch for the
different materials and wavelengths.
T −T
DoP = TE TM
(4)
TTE + TTM
A degree of polarization of –1 signifies fully TM polarized radiation, +1 signifies fully TE polarization, and 0 means
equal TE and TM polarization.
The masks were modeled at all of the wavelengths listed for the specific material in Tables 2 and 4. All masks were
modeled with the light incident at 0 degrees, except for the binary mask, which was also modeled for an off axis
illumination of NA = 1.2 and magnification of 4x which corresponds to 16.9 degrees in air, 11.5 degrees in quartz.
4. RESULTS
If the Wood’s Anomaly equation is rearranged into equation 5, the grating pitch at which a particular order emerges is
given.
m⋅λ
Λ=
(5)
n ± sin θ
For all on axis cases in this experiment, this corresponds to the first order emerging at Λ = λ . For all APSM material
cases, the 0th order (Figures 3,5,7,9,11,13,15,17,19) experiences a sharp decrease in transmission at Λ = λ . The on-axis
illumination of the binary mask also has its first orders emerging at a mask pitch equal to λ however it does not
experience the same sharp drop in transmission.
Overall, for materials with similar n and k values, the transmission and degree of polarization (DoP) results are quite
similar. To prevent great repetition in the analysis, TaO5-SiO2 and MoO3-SiO2 will be considered together for the
157nm illumination case, and TaN-Si3N4 and Si-Si3N4 for the 193 and 248nm cases.
The APSM materials act as relatively efficient polarizers when illuminated with 157nm radiation (Figures 3-6). Below
Λ=λ, they have the highest 0th order transmission. At a Λ very near λ, they are very efficient polarizers, passing 100%
TM polarized radiation. However, this is also where the +/-1st orders emerge and transmission drops to a minimum,
below 5%. As mask pitch increases, so does transmission, while the TM polarization efficiency decreases. The DoP for
the +/-1st orders remains near 0 except in the region where λ<Λ<2λ, where more TM polarization is passed. At Λ = 2λ,
the mask passes equal TE and TM polarized radiation.
For 193nm radiation (Figures 7-12), the APSM materials’ transmission follows the same trends that the 0th and 1st
orders followed in the 157nm case. The 0 order is transmitted most below Λ=λ, is a minimum at approximately Λ=λ,
and increases slowly to 10% as Λ increases. The 1st orders emerge at Λ=λ, and the transmission slowly increases until
Λ=2λ where it levels off at about 17%. For TaN-Si3N4 (Figure 7) and Si-Si3N4 (Figure 9) the 0th order is polarized
predominantly TM, with maximum efficiency of DoP close to –1 just above and below Λ=λ. At Λ=λ, there is a sharp
decrease in polarization efficiency. The 1st orders (Figures 8 and 10) are polarized predominantly TM (maximum DoP
near –0.5) at Λ=λ, and essentially decrease in efficiency linearly with mask pitch until Λ=2λ, where they are polarized
equally 50% TE and 50% TM. For the MoO3-SiO2 case, the 0th order (Figure 11) is polarized predominantly TM,
however, just below Λ=λ there is a sharp decrease in efficiency towards DoP=0, followed by a sharp increase in
efficiency until DoP=-1 at a Λ slightly greater than λ. Polarization efficiency steadily decreases as Λ becomes greater.
The 1st orders (Figure 12) are polarized slightly more TM (between DoP of 0 and –0.2) at Λ=λ and remain so until
Λ=2λ where the polarization efficiency decreases back to DoP=0. For the 248nm illumination of the APSM materials
(Figures 13-18), all results follow the same trends from the 193nm case with a few slight differences in the extrema.
In the case of the 193nm on-axis illumination of the binary CrxOyNz mask (Figures 19 and 20), the 0th order
transmission decreases to a minimum of just under 15% as Λ approaches λ., then increases sharply to just above 20% at
Λ=λ, after which it continuously increases to slightly over 25% at Λ=1000nm. The 0th order DoP is approximately –0.5
(75% TM, 25% TE) until Λ=λ, at which it rapidly loses efficiency and briefly acts as an inverse polarizer, and then
remains close to 0 from just past Λ=λ to Λ=1000nm. The +/-1st orders arise at Λ=λ and consistently transmit 6-7% until
Λ=2λ where their transmission increases to and remains at about 8%. The +/-1st orders are polarized predominantly TE
(DoP ~0.2) at Λ=λ, and slowly loses efficiency as Λ increases.
For 193nm off-axis illumination of the binary CrxOyNz mask (Figures 23, 25, and 27), the 0th order transmission follows
a similar trend to that in the 193nm on-axis case, however it increases sharply at there both the +1st and –1st orders
emerge, which is at Λ=3λ/4 and Λ=3λ/2 respectively. After the +1st order begins to propagate, the transmission slowly
increases towards 25% as Λ approaches 1000nm. The 0th order is polarized predominantly TM (DoP=-0.5) below the
mask pitch at which the –1st order emerges. At this pitch the 0th order rapidly loses polarization efficiency to a DoP of
about –0.2, where it remains relatively constant until the mask pitch approaches the pitch at which the +1st order
emerges. At this pitch there is again a rapid decrease in the polarization efficiency, for a brief period the mask acts as a
weak inverse polarizer, and then passes equal amounts of TE and TM past a pitch of 400nm. The –1st order
transmission is roughly 5% from Λ=3λ/4 until the +1st order emerges at Λ=3λ/2, where it rises sharply and remains
relatively constant at approximately 7%. The –1st order is polarized more TE than TM and reaches its maximum
polarization efficiency at a DoP=0.4 at Λ=3λ/2 where the +1st order emerges, then loses efficiency and approaches a
DoP=0 as pitch increases. The +1st order emerges at Λ=3λ/2 and increases in transmission from 5% to 9% at Λ=3λ,
after which it remains steady. It is polarized slightly TM until it’s maximum TM polarization efficiency at about Λ=2λ,
and becomes slightly more TE polarized as pitch increases until it reaches its maximum TE polarization efficiency with
a DoP=0.09 near Λ=3λ, after which DoP decreases back towards 0 as pitch increases.
Besides some subtle differences, the 248nm on-axis illumination of the binary CrxOyNz mask (Figures 21 and 22)
generates very similar trends to the 193nm on-axis case for transmission and polarization efficiency. One notable
difference is that the 0th order has greater extrema. The 0th order transmission begins higher at a value near 30%, then
sharply drops to near 10% at Λ=150nm, and then increases with mask pitch to near 25% transmission at Λ=1000nm.
The 0th order has a DoP of about –0.9 at the minimum pitch and loses efficiency until Λ=λ where it briefly acts as a
weak inverse polarizer, and at larger pitches is polarized equally TE and TM. The +/-1st orders emerge at Λ=λ and
follow similar trends as in the 193nm on-axis case. Overall, the transmission of the orders is 1-2% greater than in the
193nm case. The DoP begins slightly more TM, but within a pitch increase of λ/5, the DoP becomes slightly more TE
with a maximum DoP of 0.12 just before Λ=2λ. The mask loses polarization efficiency as pitch increases and slowly
moves towards a DoP of 0.
For the 248nm off-axis illumination of the binary CrxOyNz mask (Figures 24, 26, and 28), very similar patterns to the
193nm off-axis illumination case are observed. The –1st and +1st orders emerge at Λ=3λ/4 and Λ=3λ/2. The 0th order
transmission is very similar to the 248nm on-axis case, but with sharp increases as the +/-1st orders emerge, as in the
193nm off-axis case, but with a less-sharp increase with the emergence of the +1st order. The +/-1st order transmissions
are very similar to the 248nm on-axis 1st order transmissions, except the +1st order exhibits slightly greater
transmissions (1%). As in the 193nm of-axis case, the –1st order is polarized more TE than TM and reaches its
maximum polarization efficiency at a DoP of about 0.2 at near Λ=3λ/2 where the +1st order emerges, then loses
efficiency and approaches a DoP=0 as pitch increases. However, the –1st order is polarized more TM where it first
emerges, then steadily loses its TM polarization efficiency within a change in pitch of λ/5 after which it functions as
mentioned above. The +1st order’s polarization follows the same patterns as in the 193nm off-axis case, but exhibits its
maximum TM polarization when it first emerges, steadily loses TM polarization efficiency until Λ=2.5λ where the
DoP=0, then TE polarization slightly increases until it reaches a maximum DoP at Λ=3λ, after which as pitch increases
the DoP moves towards 0.
Tables 5 and 6 offer summaries of the degrees of polarization for different illumination schemes for different masks at
the NA values mentioned in the introduction. The polarization effects induced by the mask at the higher NA are always
greater in magnitude than at the lower NA, except for three cases (CrxOyNz mask 193nm off-axis illumination +1st order
and CrxOyNz mask 248nm on-axis and off-axis illumination 0th order).
DoP
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
Degree of Polarization
0.2
-1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-1
0.9
0
0.0
0.1
0.2
0.3
0.4
Mask Pitch (um)
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 3. Ta2O5-SiO2 mask, 0th order results for 157nm
illumination.
DoP
0.5
Figure 4. Ta2O5-SiO2 mask, +/- 1st order results for 157nm
illumination.
Unpolarized Transmission
DoP
Unpolarized Transmission
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Degree of Polarization
0.6
Unpolarized Transmission
0.2
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Mask Pitch (um)
Figure 5. MoO3-SiO2 mask, 0th order results for 157nm
illumination.
Figure 6. MoO3-SiO2 mask, +/- 1st order results for 157nm
illumination.
Unpolarized Transmission
0.0
Degree of Polarization
Unpolarized Transmission
0.6
Unpolarized Transmission
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
Degree of Polarization
0.2
-1
-1
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
0.0
0.9
0.1
0.2
0.3
0.4
Figure 7. TaN-Si3N4 mask, 0th order results for 193nm
illumination.
0.7
0.8
0.9
Figure 8. TaN-Si3N4 mask, +/- 1st order results for 193nm
illumination.
Unpolarized Transmission
DoP
Unpolarized Transmission
0.6
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
-1
Degree of Polarization
0.2
Unpolarized Transmission
Degree of Polarization
0.6
Mask Pitch (um)
Mask Pitch (um)
DoP
0.5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-1
0.9
0
0.0
0.1
0.2
0.3
0.4
Mask Pitch (um)
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 9. Si-Si3N4 mask, 0th order results for 193nm
illumination.
DoP
Figure 10. Si-Si3N4 mask, +/- 1st order results for 193nm
illumination.
Unpolarized Transmission
DoP
Unpolarized Transmission
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
-1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 11. MoO3-SiO2 mask, 0th order results for 193nm
illumination.
Degree of Polarization
0.6
Unpolarized Transmission
0.2
0.0
Unpolarized Transmission
0.1
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 12. MoO3-SiO2 mask, +/- 1st order results for 193nm
illumination.
Unpolarized Transmission
0.0
Degree of Polarization
Unpolarized Transmission
0.6
Unpolarized Transmission
DoP
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
Degree of Polarization
0.2
-1
-1
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
0.0
0.9
0.1
0.2
0.3
0.4
Figure 13. TaN-Si3N4 mask, 0th order results for 248nm
illumination.
0.7
0.8
0.9
Figure 14. TaN-Si3N4 mask, +/- 1st order results for 248nm
illumination.
Unpolarized Transmission
DoP
Unpolarized Transmission
0.6
0.2
0.6
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
-1
Degree of Polarization
0.2
Unpolarized Transmission
Degree of Polarization
0.6
Mask Pitch (um)
Mask Pitch (um)
DoP
0.5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-1
0.9
0
0.0
0.1
0.2
0.3
0.4
Mask Pitch (um)
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 15. Si-Si3N4 mask, 0th order results for 248nm
illumination.
DoP
Figure 16. Si-Si3N4 mask, +/- 1st order results for 248nm
illumination.
DoP
Unpolarized Transmission
Unpolarized Transmission
0
0.5
0
0.5
-0.2
0.4
-0.2
0.4
-0.4
0.3
-0.4
0.3
-0.6
0.2
-0.6
0.2
-0.8
0.1
-0.8
0.1
-1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 17. MoO3-SiO2 mask, 0th order results for 248nm
illumination.
Degree of Polarization
0.6
Unpolarized Transmission
0.2
0.2
0.0
Unpolarized Transmission
0.1
-1
0.6
Unpolarized Transmission
0.0
Degree of Polarization
Unpolarized Transmission
0.6
Unpolarized Transmission
DoP
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 18. MoO3-SiO2 mask, +/- 1st order results for 248nm
illumination.
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-0.8
-1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-0.8
-1
0
0.0
0.3
0
0.0
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Mask Pitch (um)
Figure 19. Binary Cr-O-N mask, 0th order results for 193nm
illumination.
Figure 20. Binary Cr-O-N mask, +/- 1st order results for
193nm illumination.
DoP
0.3
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
Degree of Polarization
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.4
0.05
-0.8
-1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.3
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-0.8
-1
0
0.0
Unpolarized Transmission
0.4
0
0.0
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Mask Pitch (um)
Figure 21. Binary Cr-O-N mask, 0th order results for 248nm
illumination.
Figure 22. Binary Cr-O-N mask, +/- 1st order results for
248nm illumination.
DoP
0.3
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-0.8
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 23. Binary Cr-O-N mask, 0th order results for 193nm
off-axis illumination.
Degree of Polarization
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.4
Unpolarized Transmission
0.25
0
Unpolarized Transmission
0.4
Unpolarized Transmission
0.4
0.3
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
Unpolarized Transmission
0.2
Degree of Polarization
0.3
Unpolarized Transmission
DoP
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.4
0.05
-0.8
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Figure 24. Binary Cr-O-N mask, 0th order results for 248nm
off-axis illumination.
DoP
0.3
0.2
0.25
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
Degree of Polarization
0.4
0.05
-0.8
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-1
0.9
0
0.0
0.1
0.2
0.3
Mask Pitch (um)
DoP
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
0.05
-0.8
-1
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Degree of Polarization
0.2
Unpolarized Transmission
0.3
0.1
0.6
0.7
0.8
0.9
Figure 26. Binary Cr-O-N mask, -1st order results for 248nm
off-axis illumination.
Unpolarized Transmission
0.4
0.0
0.5
Mask Pitch (um)
Figure 25. Binary Cr-O-N mask, -1st order results for 193nm
off-axis illumination.
DoP
0.4
Unpolarized Transmission
0.4
0.3
0.2
0.25
0
0.2
-0.2
0.15
-0.4
0.1
-0.6
Unpolarized Transmission
0.1
0
-0.8
0
0.0
Degree of Polarization
Unpolarized Transmission
0.3
Unpolarized Transmission
Unpolarized Transmission
Unpolarized Transmission
Degree of Polarization
DoP
0.4
0.05
-0.8
-1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mask Pitch (um)
Mask Pitch (um)
Figure 27. Binary Cr-O-N mask, +1st order results for 193nm
off-axis illumination.
Figure 28. Binary Cr-O-N mask, +1st order results for 248nm
off-axis illumination.
Wavelength
157nm
193nm
248nm
Order
0th
1st
0th
1st
0th
1st
NA
0.85
1.2
0.85
1.2
0.85
1.2
0.85
1.2
0.85
1.2
0.85
1.2
-0.353 -0.671 -0.006 -0.07
x
x
x
x
x
x
x
x
Ta2O5
x
x
x
x
-0.297 -0.442 -0.013 -0.107 -0.298 -0.476 -0.008 -0.102
TaN
x
x
x
x
-0.304 -0.471 -0.009 -0.102 -0.299 -0.484 -0.007 -0.1
Si
-0.354 -0.698 0.004 -0.087 -0.351 -0.709 0.013 -0.102 -0.353 -0.703 0.006 -0.089
MoO3
Table 5. Degree of polarization values for particular NA for APSM materials.
Wavelength
Order
0th
NA
0.85
1.2
-0.004 0.018
Cr-O-N
Cr-O-N OAI -0.001 0.045
193nm
248nm
-1st
+1st
0th
-1st
+1st
0.85
1.2
0.85
1.2
0.85
1.2
0.85
1.2
0.85
1.2
0.12 0.171 0.12 0.171 -0.049 -0.026 0.082 0.102 0.082 0.102
0.137 0.323 -0.021
0
-0.025 -0.016 0.104 0.231 -0.042 -0.136
Table 6. Degree of polarization for particular NA for binary Cr-O-N mask.
5. CONCLUSION
Rigorous Coupled Wave Analysis was used to solve Maxwell’s equations for photomasks comprised of alternating
phase shift mask materials and for a standard binary CrxOyNz-on-glass. Different materials, radiation wavelength,
thickness, pitch, and incident angle all have a great effect on how much a mask will polarize light.
The APSM materials tend to act more like traditional wire-grid polarizers and pass mainly the TM component and for
all of the cases a higher NA results in greater polarization. For the binary CrxOyNz-on-glass mask materials, higher NA
usually results in a greater polarization contribution from the mask. Additionally, the binary mask material also acts as
an inverse polarizer in some circumstances, passing more TE polarization than TM. In the off-axis illumination case,
there is significant shadowing of the +1st order from the thickness of the mask material. This is easily seen in figures
25-28 where the +1st order does not begin transmitting until the pitch is significantly larger than in the –1st order case.
Polarization induced by the mask will need to be taken into account. Mask materials that transmit equal amounts of TE
and TM polarization are desirable as higher numerical apertures are pursued so that no one polarization state has more
weighting than the other, especially the TM state which could have a detrimental impact on image contrast. Concerns
regarding polarization mask effects may lead to requirements to increase the reduction factor of projection imaging
tools. As 4x reduction may be a concern for sub-45nm generations, 6x or 8x can reduce critical issues.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
B. Smith, J. Cashmore, Challenges in High NA, Polarization, and Photoresists.
J. H. Johnson, Wire Grid Polarizers for Visible Wavelengths, PhD dissertation, University of Rochester, Rochester,
NY, 2003
R. W. Wood, Uneven Distribution of Light in a Diffraction Grating Spectrum, Philosophical Magazine, September,
1902
Lord Rayleigh, On the Remarkable Case of Diffraction Spectra Described by Prof. Wood, Philosophical Magazine,
July, 1907
Honkanen et al, Inverse Metal-Stripe Polarizers, Applied Physics B 68, 81-85, 1999
http://www.rit.edu/~635dept5/
M. G. Moharam, T. K. Gaylord, Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction, J. Opt. Soc. Am.
71 (7), 811-818, 1981
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